Skyhawk GT-2A Frame Build questions

Hi, Sorry if this is in the wrong place, I'm new here.
Anyways, I'm starting a build with the skyhawk frame and I need help with a few questions.

1. Bottom bracket. I'm planning on using a crank set scrapped from an old Schwinn cruiser. The bearing cups fit on one side of the skyhawk frame(needing to be pressed in of course) but the other one just slides into the bracket and has a little play.
Could I just build up a little material on the cup to get it to press in? or should I find a bearing set that actually fits?

2. Head bearings. This one I can probably answer on my own when I order my forks, but here it goes. I want to use the monark type 2 forks, the question here is will I have to do some seat swapping on the forks to get it to work with the bearings provided with the bike frame?